A digital filter is integrated, miniaturized and manufactured with low cost and high reliability, and so have much advantage compared with an analog filter. Specially, application field of the digital filter has been increased according as communication velocity is realized with high speed and an amount of communication is augmented, and the digital filter has been employed in devices such as a transmitter and a receiver of a baseband module in a mobile communication system.
The digital filter is generally divided into a finite impulse response filter and an infinite impulse response filter.
The finite impulse response filter uses characteristic that impulse response has a finite length when the impulse response is inputted to the filter. This is because the finite impulse response filter does not use any feedback.
The finite impulse response filter not using the feedback does not need feedback loop, and thus stability of the filter is guaranteed. Specially, since the finite impulse response filter satisfies linear phase characteristic, the finite impulse response filter has been widely used in applications such as waveform transmission, etc. However, in case that the finite impulse response filter will realize approximately the same amplitude as the infinite impulse response filter, order of the finite impulse response filter is more increased. As a result, the finite impulse response filter is more loaded in view of hardware including an adder and a multiplier.
The finite impulse response filter may be designed through a design method in a frequency domain and a design method in a time domain, and a window function method and a frequency sampling method, etc. are mainly used when the finite impulse response filter is designed through the design method in the frequency domain.
The design of the filter in the time domain is simpler than that in the frequency domain because impulse response in the design of the filter in the time domain corresponds to coefficients of the filter. A linear programming is widely known as a method of approximating a transfer function, and an optimal solution may be calculated through finite calculation in case that the optimal solution exists.
Specially, output finitude of the finite impulse response filter allows to omit a calculation process of not generating decimated output or a calculation process of generating a predictable value in an interpolated output, and thus this is calculatedly efficient when performing interpolation or decimation so as to increase or reduce multirate application, e.g. sampling rate of a signal.
Filter Attenuation Characteristics is associated with filter response transition between pass band and stop band. Ideally, the steeper is the filter attenuation characteristics, the better is the filter characteristics. The filter attenuation characteristics is in trade-off relation with the number of taps of the filter.
In order words, in order for better attenuation characteristics, more taps are required. As the number of taps greatly affect manufacturing cost of the filter, filter implementation cost becomes more expensive if better attenuation characteristics is to be obtained.
Further, in conventional digital filters, filter coefficients and the number of taps of the filter are fixed, therefore, it was impossible to adjust pass band adaptively.